Twice evasions of Omicron variants explain the temporal patterns in six Asian and Oceanic countries

Background The ongoing coronavirus 2019 (COVID-19) pandemic has emerged and caused multiple pandemic waves in the following six countries: India, Indonesia, Nepal, Malaysia, Bangladesh and Myanmar. Some of the countries have been much less studied in this devastating pandemic. This study aims to assess the impact of the Omicron variant in these six countries and estimate the infection fatality rate (IFR) and the reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{0}$$\end{document}R0 in these six South Asia, Southeast Asia and Oceania countries. Methods We propose a Susceptible-Vaccinated-Exposed-Infectious-Hospitalized-Death-Recovered model with a time-varying transmission rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta (t)$$\end{document}β(t) to fit the multiple waves of the COVID-19 pandemic and to estimate the IFR and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{0}(t)$$\end{document}R0(t) in the aforementioned six countries. The level of immune evasion and the intrinsic transmissibility advantage of the Omicron variant are also considered in this model. Results We fit our model to the reported deaths well. We estimate the IFR (in the range of 0.016 to 0.136%) and the reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{0}(t)$$\end{document}R0(t) (in the range of 0 to 9) in the six countries. Multiple pandemic waves in each country were observed in our simulation results. Conclusions The invasion of the Omicron variant caused the new pandemic waves in the six countries. The higher \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{0}(t)$$\end{document}R0(t) suggests the intrinsic transmissibility advantage of the Omicron variant. Our model simulation forecast implies that the Omicron pandemic wave may be mitigated due to the increasing immunized population and vaccine coverage. Supplementary Information The online version contains supplementary material available at 10.1186/s12879-023-07984-9.


S1 Parameters used in the model simulation
We have introduced some parameters of S-S V -E-I-H-D-R model in the main text. We here introduce the data and some other parameters in the model simulations process. In Table S1, the population is the whole population in each country at the time when we started our study. We assume the population is constant during our study period. The Log likelihood value is the current optimal outcome of our codes. The Log likelihood value standard derivation is the standard derivation of the The Log likelihood value we computed ten times under the optimal condition.  In Table S2, ϕ is the estimated infection severity case ratio. θ is the first immune evasion proportion and θ 1 is the second immune evasion proportion. θ and θ 1 represent how much loss of immunity for the recovered (R) and vaccinated (V) at time t 1 and t 1 + 120 days, respectively. We presume the second invasion occurred at t 1 + 120 days for simplicity. α is the relative ratio of Omicron IFR vs pre-Omicron IFR. t 1 is the Omicron first invasion time in each country. For example, t 1 = 2021.97695 in India, this means the Omicron first invasion time is on the day 0.97695×365, 2021. τ is the over dispersion, which appears in the Z t+∆t ∼ N egative Binominal(mean = D t+∆t , variance = D t+∆t (1 + τ D t+∆t )). ∆t in this equation is the τ . BS.0, BE.0, BI.0, BT.0, BD.0 and BR.0 are the system state initial values.
The data and parameters listed in Table S1-Table S3 as an example to show what kind of detailed information we need to get the results in the main text. Actually, one of the result (Scenario 4, Fig.S4) in the next section is generated using these data and parameters. There would be some minor changes or adjustments to the parameters when we want to set different assumptions and fit different scenarios. Table S4 shows the ratio between excess mortality rate and reported COVID-19 mortality rate [6].

S2 Literature Statistics
We selected six countries as our research objects. And, we think some of these countries are less studied in the previous studies. We want to show this statement via the specific statistics shown in Table S5. We chose the different phrase combining with different country names as the search keywords. Then we applied google scholar to search these keywords and to get the total literature numbers.
Here we set India as an example to explain this search process. 'Country name COVID-19 Mathematical Modeling (Anywhere in the article)' mow means that the search keywords are 'India COVID-19 Mathematical Modeling' with the search setting 'Anywhere in the article'. After this search, we find there are 46,100 papers include the keywords 'India COVID-19 Mathematical Modeling' anywhere in the articles.
From Table S5, we can see that Nepal, Malaysia, Bangladesh and Myanmar obviously are the less studied countries in the previous studies.

S3 The results under different scenarios
To test the sensitivity and consistency of our model,we set the different assumptions and scenarios to fit the model. We list several of them as following: • Scenario 1: Consider "a single" invasion scenario of Omicron variants, to fit the transmission rate β(t) (in the unit of R 0 (t)) with 17 cubic spline nodes, ψ = 1/2; • Scenario 2: Consider "a single" invasion scenario of Omicron variants, to fit the transmission rate β(t) (in the unit of R 0 (t)) with 17 cubic spline nodes, ψ = 1/3; • Scenario 3: Consider multiple (e.g. "twice") invasions scenario by initial Omicron BA1 (or BA2 or both) variant and follow-up Omicron ( BA4 or BA5) variant,to fit the transmission rate β(t) (in the unit of R 0 (t)) with 17 cubic spline nodes, ψ = 1/2; • Scenario 4: Consider multiple (e.g. "twice") invasions scenario by initial Omicron BA1 (or BA2 or both) variant and follow-up Omicron ( BA4 or BA5) variant,to fit the transmission rate β(t) (in the unit of R 0 (t)) with 16 cubic spline nodes, ψ = 1/3.

S3.1 Scenario 1
In this subsection, we consider "a single" invasion scenario of Omicron variants, to fit the transmission rate β(t) (in the unit of R 0 (t)) with 17 cubic spline nodes, ψ = 1/2. The model simulation result is shown in Figure S1.

S3.2 Scenario 2
In this subsection, we consider "a single" invasion scenario of Omicron variants, to fit the transmission rate β(t) (in the unit of R 0 (t)) with 17 cubic spline nodes, ψ = 1/3. The model simulation result is shown in Figure S2.

S3.3 Scenario 3
In this subsection, we consider multiple (e.g. "twice") invasions scenario by initial Omicron BA1 (or BA2 or both) variant and follow-up Omicron ( BA4 or BA5) variant,to fit the transmission rate β(t) (in the unit of R 0 (t)) with 17 cubic spline nodes, ψ = 1/2. The model simulation result is shown in Figure S3.

S3.4 Scenario 4
In this subsection, we consider multiple (e.g. "twice") invasions scenario by initial Omicron BA1 (or BA2 or both) variant and follow-up Omicron ( BA4 or BA5) variant,to fit the transmission rate β(t) (in the unit of R 0 (t)) with 16 cubic spline nodes, ψ = 1/3. The model simulation result is shown in Figure S4.